{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "from devito import *\n",
    "from examples.seismic.source import WaveletSource, TimeAxis\n",
    "from examples.seismic import plot_image\n",
    "import numpy as np\n",
    "\n",
    "from sympy import init_printing, latex\n",
    "init_printing(use_latex='mathjax')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Initial grid: 1km x 1km, with spacing 100m\n",
    "extent = (2000., 2000.)\n",
    "shape = (81, 81)\n",
    "x = SpaceDimension(name='x', spacing=Constant(name='h_x', value=extent[0]/(shape[0]-1)))\n",
    "z = SpaceDimension(name='z', spacing=Constant(name='h_z', value=extent[1]/(shape[1]-1)))\n",
    "grid = Grid(extent=extent, shape=shape, dimensions=(x, z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class DGaussSource(WaveletSource):\n",
    "    \n",
    "    def wavelet(self, f0, t):\n",
    "        a = 0.004\n",
    "        return -2.*a*(t - 1./f0) * np.exp(-a * (t - 1./f0)**2)\n",
    "\n",
    "# Timestep size from Eq. 7 with V_p=6000. and dx=100\n",
    "t0, tn = 0., 200.\n",
    "dt = 1e2*(1. / np.sqrt(2.)) / 60.\n",
    "time_range = TimeAxis(start=t0, stop=tn, step=dt)\n",
    "\n",
    "src = DGaussSource(name='src', grid=grid, f0=0.01, time_range=time_range)\n",
    "src.coordinates.data[:] = [1000., 1000.]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#NBVAL_SKIP\n",
    "\n",
    "src.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Now we create the velocity and pressure fields\n",
    "p = TimeFunction(name='p', grid=grid, staggered=NODE, space_order=2, time_order=1)\n",
    "v = VectorTimeFunction(name='v', grid=grid, space_order=2, time_order=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "from devito.finite_differences.operators import div, grad\n",
    "t = grid.stepping_dim\n",
    "time = grid.time_dim\n",
    "\n",
    "# We need some initial conditions\n",
    "V_p = 4.0\n",
    "density = 1.\n",
    "\n",
    "ro = 1/density * dt\n",
    "l2m = V_p*V_p*density * dt\n",
    "\n",
    "# The source injection term\n",
    "src_p = src.inject(field=p.forward, expr=src)\n",
    "\n",
    "# 2nd order acoustic according to fdelmoc\n",
    "u_v_2 = Eq(v.forward, v + ro * grad(p))\n",
    "u_p_2 = Eq(p.forward, p + l2m * div(v.forward))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\operatorname{v_{x}}{\\left(t + dt,x + \\frac{h_{x}}{2},z \\right)}\\\\\\operatorname{v_{z}}{\\left(t + dt,x,z + \\frac{h_{z}}{2} \\right)}\\end{matrix}\\right] = \\left[\\begin{matrix}\\operatorname{v_{x}}{\\left(t,x + \\frac{h_{x}}{2},z \\right)} + 1.17851130197758 \\frac{\\partial}{\\partial x} p{\\left(t,x,z \\right)}\\\\\\operatorname{v_{z}}{\\left(t,x,z + \\frac{h_{z}}{2} \\right)} + 1.17851130197758 \\frac{\\partial}{\\partial z} p{\\left(t,x,z \\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Eq(Vector(v_x(t + dt, x + h_x/2, z), v_z(t + dt, x, z + h_z/2)), Vector(v_x(t, x + h_x/2, z) + 1.17851130197758*Derivative(p(t, x, z), x), v_z(t, x, z + h_z/2) + 1.17851130197758*Derivative(p(t, x, z), z)))"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u_v_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle p{\\left(t + dt,x,z \\right)} = p{\\left(t,x,z \\right)} + 18.8561808316413 \\frac{\\partial}{\\partial x} \\operatorname{v_{x}}{\\left(t + dt,x + \\frac{h_{x}}{2},z \\right)} + 18.8561808316413 \\frac{\\partial}{\\partial z} \\operatorname{v_{z}}{\\left(t + dt,x,z + \\frac{h_{z}}{2} \\right)}$"
      ],
      "text/plain": [
       "Eq(p(t + dt, x, z), p(t, x, z) + 18.8561808316413*Derivative(v_x(t + dt, x + h_x/2, z), x) + 18.8561808316413*Derivative(v_z(t + dt, x, z + h_z/2), z))"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u_p_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "op_2 = Operator([u_v_2, u_p_2] + src_p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Operator `Kernel` run in 0.04 s\n"
     ]
    }
   ],
   "source": [
    "#NBVAL_IGNORE_OUTPUT\n",
    "\n",
    "# Propagate the source\n",
    "op_2(time=src.time_range.num-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BE46C/TkVuCHNq70OuNHMvidpC7BW0v8A7qIq5Ts09Fo4xZuE3iTKMV87d+7s9G3evLnTfvjhh4HxE97nnHNOp51NMu8QKJlhUHYElKhLk2qKH2uv2LFcNw3g7rvv7rRPPPFEYHz83Zve9KZOOzsI/Hvzpmg2e72p7Z012RSti2NrM20SWE1o4v28l2o9vu7+h6kWOA2CYJoyjGlS7ZkRDYKgyKDMT0krJG1NAfefKOw/IgXij6bA/EVu31Wpf6ukS1z/GklPSrp/QI8baVL90Cs2DcZMHm/6+GOzqZjTfmC89zP/qi5evLjT572AubLFM8880+nzHsUS/v7+yztRsySfX3ed/L6899fHnnmvaDZFfRrVL/zCL3TaORbvoYce6vT52mv5fXjz008B5M+jzlQueULb4gUdhPmZpp++SDWnvh3YKGmdmW1xh10OPGNmSyStogrQ/6CkZVQrS50FnAb8QNKbU1TFV4AvAF+d8CAT7fjUgiCoZUCa2gXAqJk9bGavAGuBlV3HrKQKxAe4Cbgore25ElhrZi+b2SPAaLoeZvbPVMvpDYwQakHQcgYk1OYDj7vtUsB955gU6rUXOKnhuQMjzM8GlAoQ1nk/SwGpvspFThnK5athfOpP5swzx+KbvSma8Z6/usKJ2etZF2Ra+iL3E4Sa99fdPz+3v47PKvGe0Pw+tm7d2ulbsmRJp50DkN/4xjd2+rZt29Zp55Lm3rz1gcDZFPXP5z+3ttJnuMZcSSNue3UKnp9RhFALgpbTh/dzt5ktr9m3A1jotksB9/mY7ZJmA3OApxueOzBCqPVBnaZWWn/SawF+8jprar5ct+ekk04CxmspvkR2nlz3ieN+8ttrhfnL7Pf7X+38DHXaWdP/DHWaWr6vv05d+lhO2vfal3ckZA1t/vwxq8XHtOX4Nf+u/bvIbR+z5z+jNmttA4pT2wgslbSYSiCtYqygRWYdVSD+v1IF5t9mZiZpHfAPkv6KylGwFLhzEIMqEUItCFrOIISame2T9BFgPTALWGNmmyVdA4yY2TqqAPyvSRqlmvxflc7dLOlGYAuwD7gyeT6R9E3gbVSm73bgajObUCB/CLUgaDGDTIEys1uAW7r6PuXaLwHvrzn3WuDaQv+lAxmcI4RaA/pxFJTMGG8qZvPTm1aePCHuzSxvPmYHgTetSmlY3ePNlEzNXpPndSZp7q9Lwyqt4OTH6tftzM4Svxaod6BkZ0k2z7vb2az177pkfvZylLSRYXnOTAi1IGg5IdSCIGgVw5b7GUKthpLp1o/56X8dvUcux2Y9//zzxfu+4Q1vAMaqVsB4885X4SiNq2QKTvSXuq6KR8ks9+R34WPHPD6NKV8jF4OE8WXMs/no49xKizT72Df/LnK7zvwsPVcbCke2raxQE0KoBUHLCaEWNKK0qIdv+195H9meJ/r9+pmerH3UrQuatZ467agUh9YP/dQYK/1nqYtZK1Eqve01Ua+15ef2cW5+QZucsF6nVfYqXd5mhu2ZQ6gFQcsJoRYEQWsYxiKRjYVaqqc0Auwws3endIm1VFn4m4DfSiVJWkcvM6pUl8v/OpbMx7rzs9npE+L9+aUkdU9pcnuyfqnzGOrqtZXMX7/fO1hyLJ6vDedjzvJ7884Fb4rm83vVjos4tfbTz6TLR6kWXMnECu1BMAMYtoVXGgk1SQuA3wCuT9uiWqH9pnTIDcB7J2OAQRBMjGETak3Nz78GPgbkIKGTaLhCe5uo8yb2Mk+9yVOKIyvFvPUyo5qsAFUyhQdJqZx3P95P/4yl2LDSu6qLFezl6R22eSVPmwRWE5qs+/lu4Ekz23QwN5B0haQRSSOlwNEgCCaPplpamwRfE03trcB7JP06cCRwHPB5Gq7QnipnrgaYN2/ejH5zdb/2vb4QddkHpeuWIt/rFgg5UF+TcU2UXhkFve5fmrTv9a5KsWfd7RIzNSNgEAybltrzkzazq8xsgZktoqqPdJuZ/SaxQnsQzAiGTVObyM/Xx4E/SQXhTmLIVmgPgpnCsAm1voJvzex24PbUHpoV2nt94KWJcm/u+JgznxpUOj/PO/rYtJJJVlfDrGRm9ZP61A+l2K+6RV5K+/0z5IR1/658TFp+b75GWql0t79naY3PknOizbRNYDUhMgqCoOWEUAuCoFWEUAsaUed5K63glCtIwFgJ67o0qFwPzIe/+LLX2QyrC48pxa9NtPJGHf14Ykv4lLH8Dny9NF9TLj/33r17O30+pSpXQqmLk8tm5zCYnN0MyvspaQVV5MMs4Hozu65r/xHAV4HzqZbG+6CZPZr2XUWVdfQq8Edmtr7JNQ+G4fVzB8EQMKg4tZT7/UXgXcAy4FJJy7oOuxx4JqVOfo4qlZJ03CrgLGAF8LeSZjW8Zt+EplZD6Re/LkaqVGHVawQ+8TrXS/Maia8b9uSTT+7XN2fOnE47J7x7Ta0uSbxX8ntT6rSfUkaBp9f9fcJ6vobXzk4++eROO2u+vmKwr3Kbr1X3LkqZGr3i/9oS2zYg8/MCYDQ5CJG0FlhJtexdZiXw56l9E/CFlFK5ElhrZi8Dj6SIiexk7HXNvmnHpxYEQS0DCumYDzzutkupkZ1jUlD+Xqpwr7pzm1yzb0JTC4KW04emNlfSiNtenTKCZhQh1BpQMrN6mZ8eH2+V16qcO3dup8+bmqX1LxcuXNhpZ6eBN73q4sRKX+aSSVWXPF+6fqm/V5qUv75/P7m0OYyZh36907wGqr9XXje1u51j1vxYvLOmVG9tGJwG1l+RyN1mtrxm3w5godsupUbmY7ZLmg3MoXIYHOjcXtfsmzA/g6DlDMj83AgslbRY0uFUE//ruo5ZR5UyCVUK5W1WXXgdsErSEam47FLgzobX7JvQ1IKg5QzCUWBm+yR9BFhPFX6xxsw2S7oGGDGzdVSpkl9LjoA9VEKKdNyNVA6AfcCVZvYqQOmaEx1rCLU+qDM/fbxVbnszy8ekZfPztNNO6/T9+Mc/7rSzSTU6OtrpO/PMMzvt7P30Jq2Pc/MmVx5DnfeyZJaUyoH3Ml/qzLicuuRNPp/a5D24J5xwAgBLly7t9HkTPcekebN89+7dnXaOU+tlfnqPaFu8m70YVPCtmd0C3NLV9ynXfgl4f8251wLXNrnmRAmhFgQtJzIKgv3ox1GQtSavPZUcBYsWLer0+Qnx7Ch48MEHO31nnXVWp33GGWcA47MMvNPAU1ot3msnJQ2sH+2ltJZmL0dD3cr0+X3k54Px7+2RRx4B4LHHHuv0eQdL/gz8OT6To+QoGAYioT0IgtYxbEUiQ6gFQcsJTS2opc789DW+8oR1/hfGm0E5PeqNb3xjp2/JkiWddk6T8mbW3Xff3WnnNKLjjjuu0+dN3VKi+2T9UpfKeXtTPL8vnw7lx+cdAeeddx4w/r34OLZt27YB8Oijj3b6nnvuuU47m5U+Jc3XrusnTq1tJmoItSAIWkPMqQVB0DpCqBWQ9CjwPFUtpH1mtlzSicC3gEXAo8AHzOyZyRnm9KPO+5nj1LzJ5U2i3D711FM7fd67mb2fPk7t3nvv7bSz+Xnuued2+rzHrxQT5mPDSubhRL/0JfMbxt6B7/MVR/wznHPOOcD4mL5scgJs2VIVbti5c2enzz9Lfgd15mf2BA9DalQ3wybU+pk8+DUzO8/lhn0CuNXMlgK3pu0gCKYZr732WqO/tjCRGdGVwA2pfQPw3okPJwiCQTKoIpEziaZzagb8kyQD/i6VIznFzLIt8ARwymQMcDpR98H7X7nsiaxLB8peOF8k0ns/c0CpP/+pp57qtEdGRvYbi08t8l7RnFLl04V6pXT1WljZm5q57c1L74nNpp73cvqxnn/++Z12TpPavn17p897fXMqWamyh39Wb356U7aX+dk2j6enTQKrCU2F2q+Y2Q5JbwA2SHrQ7zQzSwJvPyRdAVwB4/8jB0EwNYRQK2BmO9K/T0q6maoU7y5Jp5rZTkmnAk/WnLsaWA0wb9681rzdXjFrXnvxC4RkrcmnOfmy1WeffTYwXqO65557Ou2cEuX7/PV97bVcOtxrL3XrkZaeK7dL63P6fq8JHnPMMZ121r78mE4//fT99sOYA8A7Re67775O2yevl+5V0tT8uNqsifVi2IRaz09a0jGSjs1t4GLgfsbXTroM+O5kDTIIgoMjF4kcJkdBE03tFODmNBcxG/gHM/tHSRuBGyVdDjwGfGDyhhkEwcEybJpaT6GWVno5t9D/NHDRZAxqplEyRb356E2f0qpG3mTKddbq6rHl+DU/Ye5Th7wpms3abIbC+Ji2fN26EuC539+/1PbX9PfKDgJvXvvYsccfH1tz46GHHgJg8+axGoG+dlo2e7OZCeNN+DyGknOgjmExSUOoBUHQKkKoBUHQKkKoBX1T5wnNeFM0x6zVmXzZPPPlvr2ZlMNivGnmq1X49Kwc3+Zj3np5DEvmpTcZfcWRfL6/Zskk9CZxTgPrfoZsQu/atavT503wfA9/L9/O4/ImZ5sXKG5K2wJrmzBcn3AQDCFT4f2UdKKkDZK2pX9PqDnusnTMNkmXuf7zJd0naVTS36SV3ZH0fkmbJb0mqW75vnGEpjZg8q9iXRS+15q6z4HyhLefaM/9PjHcr3/pHQilhU9Kpce9dlOK7fJ9pRplfvxeK8sxdb7Pj9VnSuRjS0nqMKYVekdBr3ppnmHT0DxTpKnlXPDrJH0ibX/cH5CKYFwNLKfKUtokaV0qhPEl4PeBO6gWYlkBfJ8qfOw/AX/XdCDD+0kHwZAwRbmfTXLBLwE2mNmeJMg2ACtS8P5xZvajtE7oV/P5ZvaAmW3tZyChqQVBi5nCObUmueDzgcfd9vbUNz+1u/sPihBqk4T/InmTKuPN0FISeWklJBhzFJT6YLz5mZ0GPsnck02yusn1/Ax15nO+rn9Wf2y+vx+TX03KOzUy3uQs1aGrey/DbF72og+hNlfSiNtendIcAZD0A2De/qfxya771eaCTwUh1IKg5fThBNjt6iXuh5m9o26fpCa54DuAt7ntBcDtqX9BV/8ODpL4eQuCFjOF9dSa5IKvBy6WdELyjl4MrE9m63OSLkxez9+uOb8RoalNASVTtC62Lbe9yVgqS+29oz42zB+bK4X4OLk6U7REaaz+Wnms3uQs1WvzFUv8sSWvqjcv/bPktjeVe5mcYZJWTNGc2nUUcsFTGMYfmNmHzWyPpE8DG9M515hZXpH6D4GvAEdReT2/n87/j8D/Ak4G/q+ku83skgMNJIRaELScqRBqdbngZjYCfNhtrwHW1Bx3dqH/ZuDmfsYSQm2KKcWxebJWU4ongzFNxWs5Hq/JlLQbr+Hle5QWY6nbX6ryWxeTl8/zGlNJ6/TP45/Lt5sunBLa2f4MW0ZBCLUgaDkh1IIgaA25SOQwEULtEFHnKCitxenNv2yGeZPUm1ylOLNSjTTfrkuj6jXWEr0m8n1fqc5cXcxcmJ0HT2hqQRC0ihBqQRC0ihBqBSQdD1xP5XI14PeArcC3gEXAo8AHUpJq0CelL12dxzG360yzkhlWZzKWzNMSva7fy/RrMtbcH2bmYIl6avV8HvhHMzuTar2CBxgrNbIUuDVtB0EwzYgV2ruQNAf4VeB3AMzsFeAVSSsZy+O6gSqH6+P7XyHoh15frqzB1Wk/XsMraT2l65fW+vT00q56UXdc0/O77xv0x7B5P5t8UxYDTwF/L+kuSden9T+blBoJguAQM2yaWhOhNhv4ReBLZvYW4AW6TM1U2K34ViRdIWlE0kiuzx8EwdQwhQnt04YmjoLtwHYzuyNt30Ql1JqUGiHVY1oNMG/evPa8uSmk1xduKr+Q/cSOHQxhZg6eNgmsJvT8BpnZE8Djks5IXRcBW2hWaiQIgkNMaGpl/ivwDUmHAw8Dv0slEPcrNRIEwfRi2BwFjYSamd1NtQJMN/uVGgmmhqn4Zc2m4GT9pwhTc/JpmxbWhMgoCIKWE0ItCIJWEUItCLqoMxN7maVhXk4PQqgFQdAqQqgFQUNCE5v+DGORyPhWBkHLmYo4NUknStogaVv694Sa4y5Lx2yTdJnrP1/SfZJGJf1NWioPSX8p6UFJ90q6OVUMOiAh1IKg5UxR8G3Pqj2STgSuBn4JuAC42gm82g+oAAAIIklEQVS/LwG/DyxNfytS/wbgbDM7B/gxcFWvgYRQC4KWM0VCbSVVtR7Sv+8tHHMJsMHM9qTaixuAFSnN8jgz+1HKI/9qPt/M/snM8hJlP2L8Su5FYk4tCFpMnwJrrqQRt7065W43oUnVnvnA4257e+qbn9rd/d38HlVh2gMSQi0IWk4fQm23mZUyhwCQ9ANgXmHXJ7vuZ5IG6nKV9ElgH/CNXseGUAuCljMo76eZvaNun6QmVXt2MFZYFipT8vbUv6Crf4e79u8A7wYusgYSOubUgqDlTNGcWpOqPeuBiyWdkBwEFwPrk9n6nKQLk9fzt/P5klYAHwPeY2aNCjKGUAuCFjOFRSKvA94paRvwjrSNpOWSrk9j2QN8GtiY/q5JfQB/SLW40yjwEPD91P8F4Fhgg6S7Jf3vXgMJ8zMIWs5UZBSY2dMUqvaY2QjwYbe9BlhTc9zZhf4l/Y4lhFoQtJxIkwqCoFUMW5pUCLUgaDFRJDIIgtYxbEKtp/dT0hnJ65D/npP0x00TWIMgOLQM28IrTVaT2mpm55nZecD5wM+Am2mQwBoEwaEnhNqBuQh4yMweo1kCaxAEh5hhE2r9zqmtAr6Z2k0SWIMgOIREkcgDkNb8fA/wf7r3pXysoqiXdIWkEUkjP/tZoyyHIAgGyLBpav2Yn+8C/s3MdqXtXSlxlQMksGJmq81suZktP/rooyc22iAI+iaEWj2XMmZ6QrME1iAIDjEh1ApIOgZ4J/Ad111MYA2CYPowhQnt04ZGjgIzewE4qauvmMAaBMH0ok0CqwmRURAELWfYvJ8h1IKg5YSmFgRBa2jbfFkTQqgFQcsJoRYEQasIoRYEQasYNkdBLLwSBC1mquLUmpYik3RZOmabpMtc//mS7pM0Kulv0qpSSPq0pHtT2bN/knRar7GEUAuCljNFwbc9S5FJOhG4Gvgl4ALgaif8vgT8PrA0/a1I/X9pZuek0mffAz7VayAh1IKg5UyRUGtSiuwSYIOZ7TGzZ4ANwIqUO36cmf0oFcf4aj7fzJ5z5x9DTeEMT8ypBUHL6UNgzZU04rZXm9nqhuc2KUU2H3jcbW9PffNTu7sfAEnXUi1wvBf4tV4DCaEWBC2nD6G228yW1+2U9ANgXmHXJ7vuZ5IG5nI1s08Cn5R0FfARKhO2lhBqQdBiBlkk0szeUbdP0i5Jp5rZzgOUItsBvM1tLwBuT/0Luvp3FM7/BnALPYRazKkFQcuZojm1JqXI1gMXSzohOQguBtYns/U5SRcmr+dv5/MlLXXnrwQe7DWQ0NSCoOVMUfDtdcCNki4HHgM+ACBpOfAHZvZhM9sj6dPAxnTONWa2J7X/EPgKcBTw/fQHcJ2kM4DX0nX/oNdAQqgFQcuZCqFWV4rMzEaAD7vtNcCamuPOLvT/537HEkItCFpMJLQHQdA6QqgFQdAqIvezgKT/JmmzpPslfVPSkZIWS7oj5Wp9Ky2hFwTBNGPY1ijoKdQkzQf+CFhuZmcDs6gWNf4M8DkzWwI8A1w+mQMNgqB/hnHhlaZxarOBoyTNBo4GdgJvB25K++tyvYIgOMSEUOvCzHYA/xP4CZUw2wtsAp41s33psHG5Wp5YoT0IDi0h1LpIkb8rgcXAaVSZ8isOeJLDYoX2IDikvPbaa43+2kIT7+c7gEfM7CkASd8B3gocL2l20tbqcrXGsWvXrt2f/exnXwB2T2DM05W5xHPNFNr4TFA91zFdfetTfxNa8U6aCLWfABdKOhp4kSpqeAT4IfA+YC31uV7jMLOTJY0cqBLATCWea+bQxmeCznMt8n1m1tiqagtN5tTuoHII/BtwXzpnNfBx4E8kjVKt3v7lSRxnEARBIxoF35rZ1exf7uNhqpK8QRAE04ZDUXqoaSXNmUY818yhjc8E7X2uvlCbXLlBEARRJDIIglYxpUJN0gpJW1O+6H5LaM0EJC2U9ENJW1I+7EdTf6N1D6c7kmZJukvS99L2jM/xlXS8pJskPSjpAUm/PNM/r8jHrmfKhJqkWcAXgXcBy4BLJS2bqvsPkH3An5rZMuBC4Mr0HD3XPZwhfBR4wG23Icf388A/mtmZwLlUzzdjP6/Ixz4wU6mpXQCMmtnDZvYKVXzbyim8/0Aws51m9m+p/TzVf5D5NFv3cFojaQHwG8D1aVvM8BxfSXOAXyWFHJnZK2b2LDP/84p87BqmUqjVrfk3Y5G0CHgLcAfN1j2c7vw18DGqevBQxR82yvGdxiwGngL+PpnV10s6hhn8eU00H7vthKPgIJH0euDbwB93rSJNWmV6RrmVJb0beNLMNh3qsQyY2cAvAl8ys7cAL9Blas60z2ui+dhtZyqF2g5godtulC86HZF0GJVA+4aZfSd170rrHXKAdQ+nM28F3iPpUaqpgbdTzUUdn0wcmJmf2XZge8qMgco8+0Vm9ufVycc2s58D4/Kx0zEz8bMaCFMp1DYCS5OH5nCqic11U3j/gZDmmb4MPGBmf+V2NVn3cNpiZleZ2YKUO7gKuM3MfpOxHF+Ymc/1BPB4WmYNqtzlLczsz6uTj52+j/mZZvRnNSimNPhW0q9TzdvMAtaY2bVTdvMBIelXgP9HlQeb557+jGpe7UbgP5DWPXRrGs4oJL0N+O9m9m5Jb6LS3E4E7gI+ZGYvH8rx9Yuk86icH4dTpff9LtUP+oz9vCT9BfBBKm/8XVTL0M1nhn9WgyAyCoIgaBXhKAiCoFWEUAuCoFWEUAuCoFWEUAuCoFWEUAuCoFWEUAuCoFWEUAuCoFWEUAuCoFX8f3zh7JWG9NgdAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#NBVAL_SKIP\n",
    "\n",
    "# Let's see what we got....\n",
    "plot_image(v[0].data[0])\n",
    "plot_image(v[1].data[0])\n",
    "plot_image(p.data[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "norm_p = norm(p)\n",
    "assert np.isclose(norm_p, .35098, atol=1e-4, rtol=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# # 4th order acoustic according to fdelmoc\n",
    "# # Now we create the velocity and pressure fields\n",
    "p4 = TimeFunction(name='p', grid=grid, staggered=NODE, space_order=4, time_order=1)\n",
    "v4 = VectorTimeFunction(name='v', grid=grid, space_order=4, time_order=1)\n",
    "u_v_4 = Eq(v4.forward, v4 + ro * grad(p4))\n",
    "u_p_4 = Eq(p4.forward, p4 + l2m * div(v4.forward))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Operator `Kernel` run in 0.04 s\n"
     ]
    }
   ],
   "source": [
    "#NBVAL_IGNORE_OUTPUT\n",
    "op_4 = Operator([u_v_4, u_p_4] + src_p)\n",
    "# Propagate the source\n",
    "op_4(time=src.time_range.num-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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IE4cq3zTfzn8cPrOFT82d1SuvpnmVKqufPtW1v39WL72Vr0r9bB9Te7su/poy9bVK/czjLvM3g5EZRbK67vO1eVU0z6GvbOUtwGXvFTnWCpoksOpQt5jxFOAh4HyK2n+PA/vNLP9njaoO465dAayAkY6ZQRCMD2H9LMHMXgMuljQduAu4oO4bpBJbKwHmzJkzKb8yyvy1qtp5BfX888+3+rwfWl6ReAHvPfLzSsb7dpUZBcoMAtB5Vdbrt7a/Pj93VQGU3ParN/9cftWW58AbWHw7z6Gf17JA/U6f0aCtWpqmWtahK+unme2XdC/w68B0SVPTaq2sskwQBBOAQRNqdayfZ6YVGpJOAt4JbATupagYA0UFme+O1SCDIDh6wlAwmrOB29K+2uuAO8zse5IeBVZL+nNgPUUlmUZTpdr4P4gcZO1Do1555ZVWO6tfXv30Ad9587vKtyyrt1Vq5liEBlXdp0zlKzMq+L6ygHgYngM/b17VzHPoj/uQrHzfqs9okGmSwKpDHevnTynKwbf3bwUuHYtBBUHQH/oZJiVpKfBlihJ5t5rZF9qOnwB8HXgLRRHjD5rZL9Kx6yncvl4D/tDM1qb+VcB7gN1mdlE/xhnFjIOg4fRD/Uya2leAdwGLgaslLW477VpgX/JdvZnCl5V03nLgQmAp8NV0P4B/SH19I8Kk+oD3Gcttr3L6b8ocEuUzUHg1KtMp9GkiZKDI71tmEfVtPz9VqcXzHPh5KXtuP68HDx5stb1/WjCSPv19XApsSRoaklYDyygKFGeWUfirAtwJ/G2qwr4MWG1mrwJPpGLHlwI/NrN/kbSgHwPMxEotCBpOFyu1WZKG3M8Kd5u5wDb3usw3tXVO8oo4AMyseW3fiK+3IGg4XazU9pjZkrEcy3gQQu0oqcqSkVUif9wnM8wWP5+Zw6tknTJrlKl8nmOhinaqUFW1UV2W6cTPi0/XXZZ63KufeQyD5j3fiT66a+wA5rvXZb6p+ZztkqYC0ygMBnWu7RuhfgZBwzl8+HCtnw48CCxK2XmOp9j4X9N2zhoKn1UofFjvSbHja4Dlkk6QtBBYBDzQtwdsI1ZqXVAV2O3786rNr168P1ZekfjVmydf38n3bCL5HnUzlk45zvy8lNVL9fPqV8id/PcGmX7Mg5kdkvQJYC2FS8cqM9sg6UZgyMzWUPiqfiMZAvZSCD7SeXdQGBUOAdel0EskfRu4nGI/bztwg5n15PMaQi0IGk4fnbDvBu5u6/uca78CvL/i2puAm0r6r+7L4Bwh1IKgwTQtBKoOIdS6oMo4UHaO3/z3tSo7pZ3OdKNGTaQ/2jKjQSc/No+fFz9veb7LjCow0heu7PggM5H+PsaDEGpB0HBCqAVB0CgGbcUaQq0GZd90ZeqOP9cnQ/Qqk1evMp3Uz8lEN6pypywa3mqc58jPn79X1edRd1xNJfbUgiBoHCHUglF0s3zPKwm/UitbXXQqltINZas/Tz/Vj7F+r6p6qmURA3UMN0e6/6AQQi0IgkYRQi0IgsbQzySRk4UQahV02ryvCvfJeb3Kgtihc761TDdpqcfzj7bX9+rkf+dVTj+HeV59kLufwzyvfq68qlmmvg6KKjpoK7Xan6qkKZLWS/peer1Q0v2Stki6PQW5BkEwwRi0wivdfFV9kqKKVOaLwM0pde8+ilS+QRBMMAZNqNWt0D4P+G2KgNQ/Til63w58KJ1yG0Ua31vGYIwThiprm+/P6pO3fvpwn1yg1xfq9XnB8h9XlWo0GSskVamcft7yc3n106vteT79NS+//HKrndXPqnnz9x00miSw6lB3T+2vgE8Bua7bTGB/StkLR0jPm1ICr4CRZeGCIBh7mrYKq0NHoSYpl696SNLl3b6Bma0EVgLMmTNnUs9uWd609nbZisCvOPLmt1+dla04qqIQylYiE2n11inzbdVqN6/EvHHglFNOabXzM7700kutvrKCN52iNwaRsH6O5m3AeyW9GzgROJ2i9t90SVPTam1M0/MGQXD0DNpKreNXmZldb2bzzGwBRSbLe8zsd4F7KVL2QpHC97tjNsogCI6aMBTU59PAakl/DqynSOU7MFQFU2eVx6tWviZlVq+8v9ULL7zQame1tFPYTx2Vc6zV0rJ/hDKjQJXK6c8tK7zi1c+yefHGlk6GgkGlaQKrDl0JNTO7D7gvtbdSFCQNgmACE0ItCIJGEUItALpLt+2PZ7WyrGYlDFdIOv3001t9zz33XKudQ386qWlVFtFONTiPRiXtJkdamaWzk08fDPvy+Xnx1aTK5rVsjjuNdRDV00Gzfg7eJxwEA0RdI0Gd1ZykpZI2pdDIz5QcPyGFTG5JIZQL3LHrU/8mSVfVvefRECu1LqgKMi8rAPLiiy+2+nzgdfbHOuOMM1p9/tzsh+X9sToZDfwfZCc/tl5VkU5+aGW+fFXj9z5peT78vPhx5zn0c+VXatkY000igEGhH+qnpCnAV4B3UjjbPyhpjZk96k67FthnZudLWk4RSvlBSYspPCcuBM4BfijpDemaTvfsmlipBUHD6dNK7VJgi5ltNbODwGpgWds5yyhCJgHuBK5IIZXLgNVm9qqZPQFsSferc8+uCaEWBA2nC6E2S9KQ+1nhbjMX2OZel4VGts5JTvkHKEIqq66tc8+uCfWzCzrl6oJh9fP5559v9R04cKDVPvvsswGYPn16q2/27NmtdlY7fRhVWe61qg33Tqpor5QZBar80HLbH/fB/V7VzHPg44P379/fauc59PPq/QOzWl/1uQwqXSaJ3GNmS8ZyPONBCLUgaDh9cunYAcx3r8tCI/M52yVNBaYBz3a4ttM9uybUzyBoOH3aU3sQWJSSwx5PsfG/pu2cNRQhk1CEUN5jxY3XAMuTdXQhsAh4oOY9uyZWal1Q5RtWlpnDW+n27NnTau/duxeAmTNntvrmzJnTaufQH2/Ze/bZZ1vtrJZWZb7oNK5u1LOyMCdPmXpZ5l/nrZxe7Z43b16rnefAX5/nCobn0M+rDz/r5L83yPRjpWZmhyR9AlgLTAFWmdkGSTcCQ2a2hiJU8huStgB7KYQU6bw7gEeBQ8B1ZvYaQNk9ex1rCLUgaDj9iigws7uBu9v6PufarwDvr7j2Jooksx3v2Ssh1GqQv/GrNufLqrH7zX2/0tqxo9gyOPPMM1t98+cPbyssWLBg1Ht58orFr+T86qZspVZl4KhLJz+0qrHmPHJ+Vbpw4cJWOz+rP3fbtmFjWJ4rGJ5Dbxwoy4xbleF2UFdtEdAeBEHjGLQwqRBqQdBwYqUW1KJqQz5vivsU3T5fWlavvD/WtGnTWu3sx1ZVN3Tr1q0A7Nq1q9XnN8875Rjr1VBQpor6e/ocaNn37Lzzzmv1efXz1FNPbbV37twJwOOPP97q86ponsOy1OhQbigICkKoBUHQGGJPLQiCxhFCrQRJvwCeB14DDpnZEkkzgNuBBcAvgA+Y2b6xGebEoCrHWlmNz6q8X9l6+fOf/7zV5/OG5euzGgojVdXs55XVUBhpJdy3b/gjyCFXXiXtFT8HOfW2D3eaO3c4dC+rneeee26rz6uPWeUE2LixqJPt58X792X10odZ+Xb+DHq19DaRQRNq3Xzqv2VmF7vYsM8APzKzRcCP0usgCCYYhw8frvXTFHr5KvNpRm4Dfqf34QRB0E/6mSRyslB3T82Af5ZkwP+yokDxbDPL+sPTwOzKqxtOmfXTV0XyGTdy5ont27e3+jr9Qb3+9a9vtd/0pjcBI9U8byX09929e/eI94SRVtmslvr39+pbVum8euzDnM466yxgZLiTdyTOTrfeOfjJJ59stdevX99qP/zww8BIVdqTLaV+Xsusn8FomiSw6lBXqP2Gme2QdBawTtJj/qCZWRJ4o0g5mVbAyL2hIAjGhxBqJZjZjvR7t6S7KDJW7pJ0tpntlHQ2sLvi2pXASoA5c+Y0ZnarjAY5yNpvYnt/rLw68sVWnnrqqVY7GxW8b5tvv+ENRRZkvzryqzZ/3xwQ7gPDOxV56VQMZcaMGaPa/rhf6WWjhd/896uzDRuGY5e9313G3zfPoZ9XH9CeCePAaAZNqHX8C5B0iqTTchu4EniEkWlGokJ7EExAcpLIQTIU1FmpzQbuSt/AU4F/NLMfSHoQuEPStcCTwAfGbphBEBwtg7ZS6yjUrKjE/uaS/meBK8ZiUJONMlXUb2L70KGyWpheJcyb/j5t9TPPPNNq5430Cy64oNXn/cBmzZrVap9zzjnAyD9qn+WiLMtGWfiXV/O8epkNIN43zqvSjz1WbL16NdOHQXkDRn4vr3L68LE8h35ewyetHiHUgiBoFCHUgiBoFCHUgr7g1SGvMnlLaNm5WSXzIUJePc1+aFm1g5FZMLxPWw618mFM3s8rhyz59/f/ADn7hy+s7FXNHObkfc98+Fbu9+qz99nzIVPZ/837wfm5ynMYamZ3NM2xtg4h1IKg4TTJslmHEGp9plPq77w6qdrkzpvyfhPd50vLqx/v17Vp06ZW2/uRZY9/3+c34nOkgB+fN2Dk6IMy3zcYjljwfb7GafaD84YGbzTxq7I8Ln+8U8RArNrqMWgrtfirCIKGMx6xn5JmSFonaXP6fUbFedekczZLusb1v0XSzyRtkfTXSt/6kt4vaYOkw5JqFVoOoRYEDWYcA9o7Zu1J6cpuAN5KEZV0gxN+twAfo6gJughYmvofAf4j8C91BxLq5xhRFUaV1Si/Se5V0ayq+eNe/cv+az4w3ecl82rp5s2bR93Lq3Q5YL1qrDmky2/u+9xw2eetLEwMhlVJH/Pr1V+vaubwJz++MvUyVM7uGSf1cxlweWrfBtwHfLrtnKuAdWa2F0DSOmCppPuA083sJ6n/6xRZf75vZhtTX+2BhFALgoYzToaCOll75gLb3OvtqW9uarf3HxUh1IKgwXSpWs6SNORer0wJKQCQ9ENgTsl1n217z8qsPeNBCLVxoEy9831ePczqm1fDyjJ+eIuo9yPzRZSzqujVx6P51q6qRpXH7cfn/eCyeun7fG62MutmlZoRaufR04VQ2+MyW5fd5x1VxyTVydqzg2EVFWAehZq6I7V9f3livRrEX0oQNJxxMhTUydqzFrhS0hnJQHAlsDaprc9JuixZPT9ScX0tYqU2zpStOMo22v15vrBLXul4b3u/ee9XanmF5ldqPqA9v29V5ts8Br/571dXue1Xan7Vmdt+/N7fLAwB48M4GQq+QEnWnuSG8V/M7KNmtlfS54EH0zU3ZqMB8HHgH4CTgO+nHyT9B+BvgDOB/yPpYTO76kgDCaEWBA1nPIRaVdYeMxsCPuperwJWVZx3UUn/XcBd3YwlhFoQNJicJHKQCKE2AeikcpWFUXk10G+++zCn7Gfm/6j9cd8uI6uKVSpjViv9ca+qxub/xGDQwqRCqAVBwwmhFgRBowihVoKk6cCtFBt5BvwBsAm4HVgA/AL4gJntq7hF0CVVqllWJb2a59v+D7jMulnVLiOrjV59LLOOdgphCTXz2DGI+dTq/rV9GfiBmV1AUa9gIzUCWIMgOPZEhfY2JE0DfhP4PQAzOwgclFQngDXoM51WPVV53MaSWIlNbAbN+lnnr3Eh8Azw95LWS7o11f+sE8AaBMExZtBWanWE2lTg14BbzOwS4EXaVE0rZqR0ViStkDQkacjHKAZBMPaMYz61CUMdQ8F2YLuZ3Z9e30kh1OoEsJKi/FcCzJkzpzkzN0EJVTBop0kCqw4d/wPM7Glgm6Q3pq4rgEepF8AaBMExJlZq5fxX4FuSjge2Ar9PIRBHBbAGQTCxGDRDQS2hZmYPA2V5lkYFsAZBMHFo2iqsDhFREAQNJ4RaEASNIoRaEASNIoRaEASNIoRaEASNIZJEBkHQOGKlFgRBowihFgRBoxg0oRaBgkHQYMYroF3SDEnrJG1Ov8+oOO+adM5mSde4/rdI+pmkLZL+OtX/RNJfSHpM0k8l3ZUS1h6REGpB0HDGKfazY9JYSTOAG4C3ApcCNzjhdwvwMWBR+lma+tcBF5nZm4CfA9d3GkgItSBoOIcPH6710yPLKJLFkn7/Tsk5VwHrzGxvSv2/DliasvycbmY/SWnMvp6vN7N/NrNcgfsnwLxOA4k9tSA5djXyAAAHvklEQVRoOOO0p1YnaexcYJt7vT31zU3t9v52/oCiLsoRCaEWBA2mS9VylqQh93plyocIgKQfAnNKrvts23uapL5KUkmfBQ4B3+p0bgi1IGg4XQi1PWZWlo0n3+cdVcck1Ukau4PhuiZQqJL3pf55bf073L1/D3gPcIXVeJjYUwuChjNOhoI6SWPXAldKOiMZCK4E1ia19TlJlyWr50fy9ZKWAp8C3mtmteoBhFALgoYzToaCLwDvlLQZeEd6jaQlkm4FMLO9wOeBB9PPjakP4OMUtYW3AI8D30/9fwucBqyT9LCkv+s0kFA/g6DBjFeSSDN7lpKksWY2BHzUvV4FrKo476KS/vO7HUsItSBoOBFR0IakN6ZlX/55TtIf1fUgDoLg2DJohVfqVJPaZGYXm9nFwFuAl4C7qOFBHATBsSeE2pG5AnjczJ6kngdxEATHmEETat3uqS0Hvp3adTyIgyA4hgxiksjaK7VU8/O9wP9uP5Yc4kpFvaQVkoYkDb30Ui03kyAI+sigrdS6UT/fBfyrme1Kr3clz2GO4EGMma00syVmtuTkk0/ubbRBEHRNCLVqrmZY9YR6HsRBEBxjQqiVIOkU4J3Ad1x3qQdxEAQTh7oCrUlCrZahwMxeBGa29ZV6EAdBMLFoksCqQ0QUBEHDGTTrZwi1IGg4sVILgqAxNG2/rA4h1IKg4YRQC4KgUYRQC4KgUYShIAiCxhB7akEQNI4QakEQNIoQakEQNIoQakEQNIpBE2pRIi8IGkxOEjnWJfLq1iyRdE06Z7Oka1z/WyT9TNIWSX+d6n8i6fOSfprqo/yzpHM6jSWEWhA0nHHK0tGxZomkGcANwFuBS4EbnPC7BfgYsCj9LE39f2Fmb0o1Ur4HfK7TQEKoBUHDGSehVqdmyVXAOjPba2b7gHXA0pRk9nQz+0nKov31fL2ZPeeuP4WKDNue2FMLgobThcCaJWnIvV5pZitrXlunZslcYJt7vT31zU3t9n4AJN0EfAQ4APxWp4GEUAuCBtPlKmyPmS2pOijph8CckkOfbXtPk9Q364SZfRb4rKTrgU9QqLCVhFALgobTL+unmb2j6pikXZLONrOdR6hZsgO43L2eB9yX+ue19e8ouf5bwN10EGqxpxYEDWc8rJ/Uq1myFrhS0hnJQHAlsDaprc9JuixZPT+Sr5e0yF2/DHis00Dq1ij4b5I2SHpE0rclnShpoaT7kwn29lRCLwiCCcY4GQpKa5ZIWiLp1jSOvcDngQfTz42pD+DjwK3AFuBx4Pv5vknu/JRCCH6y00A6qp+S5gJ/CCw2s5cl3UFR1PjdwM1mtlrS3wHXUphlgyCYIIxXQHtVzRIzGwI+6l6vAlZVnHdRSf9/6nYsddXPqcBJkqYCJwM7gbcDd6bjVSbcIAiOMYNWTaqjUDOzHcD/BJ6iEGYHgIeA/WZ2KJ02wgTriQrtQXBsCaHWRtrQWwYsBM6hcIBbesSLHBYV2oPgmDJOhoIJQx2XjncAT5jZMwCSvgO8DZguaWparVWZYEewa9euPV/60pdeBPb0MOaJyiziuSYLTXwmKJ7rlLa+tam/Do2YkzpC7SngMkknAy9TbAYOAfcC7wNWU23CHYGZnSlp6EgOfpOVeK7JQxOfCVrPtcD3mVltraop1NlTu5/CIPCvwM/SNSuBTwN/LGkLRfX2r43hOIMgCGpRK6LAzG5gtBfvVopI+yAIggnDsYgoqBsgO9mI55o8NPGZoLnP1RVqkik3CIIgYj+DIGgU4yrUJC2VtCnFi47KjDkZkDRf0r2SHk3xsJ9M/bXSGU90JE2RtF7S99LrSR/jK2m6pDslPSZpo6Rfn+yfV8RjVzNuQk3SFOArwLuAxcDVkhaP1/v3kUPAn5jZYuAy4Lr0HB3TGU8SPglsdK+/SBHjez6wjyLGd7LxZeAHZnYB8GaK55u0n5eLx15iZhcBUyjisZvwWfXMeK7ULgW2mNlWMztI4d+2bBzfvy+Y2U4z+9fUfp7iH2Qu9dIZT2gkzQN+myJbAikNzKSO8ZU0DfhNksuRmR00s/1M/s8r4rErGE+hVpXKd9IiaQFwCXA/9dIZT3T+CvgUkGNmZlIzxncCsxB4Bvj7pFbfKukUJvHn1Ws8dtMJQ8FRIulU4J+AP2orDkEqHjGpzMqS3gPsNrOHjvVY+sxU4NeAW8zsEuBF2lTNyfZ59RqP3XTGU6jtAOa717XiRSciko6jEGjfMrPvpO5dKY0xR0hnPJF5G/BeSb+g2Bp4O8Ve1PSk4sDk/My2A9tTZAwU6tmvMbk/r1Y8tpn9EhgRj53OmYyfVV8YT6H2ILAoWWiOp9jYXDOO798X0j7T14CNZvaX7lCddMYTFjO73szmpdjB5cA9Zva7DMf4wuR8rqeBbZLemLquAB5lcn9erXjs9PeYn2lSf1b9YlydbyW9m2LfZgqwysxuGrc37xOSfgP4vxRxsHnv6U8p9tXuAM4FngQ+4FIVTyokXQ78dzN7j6TzKFZuM4D1wIfN7NVjOb5ukXQxhfHjeIrwvt+n+EKftJ+XpD8DPkhhjV9PkV12LpP8s+oHEVEQBEGjCENBEASNIoRaEASNIoRaEASNIoRaEASNIoRaEASNIoRaEASNIoRaEASNIoRaEASN4v8D4V9dKQOkU2UAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#NBVAL_SKIP\n",
    "\n",
    "# Let's see what we got....\n",
    "plot_image(v4[0].data[-1])\n",
    "plot_image(v4[1].data[-1])\n",
    "plot_image(p4.data[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "norm_p = norm(p)\n",
    "assert np.isclose(norm_p, .35098, atol=1e-4, rtol=0)"
   ]
  }
 ],
 "metadata": {
  "hide_input": false,
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  },
  "widgets": {
   "state": {},
   "version": "1.1.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
